> Dedekind's Proof > by Andrew Boucher > http://www.andrewboucher.com/papers/dedekind.htm > > "In "The Nature and Meaning of Numbers," Dedekind produces an original, > quite remarkable proof for the holy grail in the foundations of elementary > arithmetic, that there are an infinite number of things. It goes like this. > [p, 64 in the Dover edition.] Consider the set S of things which can be > objects of my thought. Define the function phi(s), which maps an element s > of S to the thought that s can be an object of my thought. Then phi is > evidently one-to-one, and the image of phi is contained in S. Indeed, it is > properly contained in S, because I myself can be an object of my thoughts > and so belong to S, but I myself am not a mere thought. Thus S is infinite."
This is typical philosphical bullshit. It is the sort of thing that gives philosophy a bad name among intellectuals. While philosophers are doing this crapdoodle, mathematicians are doing real mathematics and physicists are doing honest to goodness physics.
The main difference between mathematics and philosophy can be discerned by studying how math and philsophy departments are equipped. In the math department you have pencil, paper and wastebaskets. In the philosophy department you have just pencil and paper. >